Generalized Gaussian quadrature rules for systems of arbitrary functions
SIAM Journal on Numerical Analysis
Journal of Computational Physics
On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
SIAM Journal on Numerical Analysis
A Galerkin Boundary Element Method for High Frequency Scattering by Convex Polygons
SIAM Journal on Numerical Analysis
A Refined Galerkin Error and Stability Analysis for Highly Indefinite Variational Problems
SIAM Journal on Numerical Analysis
A Sparse Discretization for Integral Equation Formulations of High Frequency Scattering Problems
SIAM Journal on Scientific Computing
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We consider the solution of high-frequency scattering problems in two dimensions, modeled by an integral equation on the boundary of a smooth scattering object. We devise a numerical method to obtain solutions on only parts of the boundary with little computational effort. The method incorporates asymptotic properties of the solution and can therefore attain particularly good results for high frequencies. We show that the integral equation in this approach reduces to an ordinary differential equation.